Bayes Factor Calculator

Formula

To calculate the Bayes Factor:

\[ BF = \frac{P(\text{Data}|H1)}{P(\text{Data}|H0)} \]

What is a Bayes Factor?

The Bayes Factor is a statistical measure that quantifies the evidence in favor of one statistical model, or hypothesis, over another. It is used in Bayesian analysis to compare the predictive power of two hypotheses, typically the null hypothesis (H0) and an alternative hypothesis (H1). The Bayes Factor can be interpreted as the strength of evidence for H1 relative to H0.

Example Calculation 1

Let's assume the following values:

Likelihood of Data under H1 \( P(\text{Data}|H1) \) = 0.8
Likelihood of Data under H0 \( P(\text{Data}|H0) \) = 0.2

Step 1: Divide the likelihood of the data under H1 by the likelihood of the data under H0:

\[ BF = \frac{0.8}{0.2} = 4 \]

Example Calculation 2

Let's assume the following values:

Likelihood of Data under H1 \( P(\text{Data}|H1) \) = 0.5
Likelihood of Data under H0 \( P(\text{Data}|H0) \) = 0.5

Step 1: Divide the likelihood of the data under H1 by the likelihood of the data under H0:

\[ BF = \frac{0.5}{0.5} = 1 \]